In the present day market, the current assembling systems, with construction toy blocks mostly commonly seen, fall under the principle of Circle Square Packing in their system of the assembling workings. However, most of their systems do not fully utilize the number of abutments provided under such principle, which defines an “existing” set of four abutting points on each of the circles abutting against each other.
If one were to image the configuration of all the circles in a Circle Square Packing like a chessboard, the packed circles will fall under two groups: the black group circles and the white group circles. Each of the black circles is situated across its neighboring white circles in a lattice, and vice versa. Also, imagine that an area encompassing a lattice of the white group circles is fixed onto a free moving flat board, and a lattice of the corresponding black group circles within the same area is fixed onto another flat board that is attached to the ground.
FIG. 1A is taking an example block representing a three-abuttment system currently seen on the market, after being assembled (or stacked up, joined) with its mating block on top of the other. For purpose of simplification, the mating block is assumed to be an identical block. This figure shows a “theoretical” cross-sectional schematic plane view, as cut at the bottom of the upper block. The rectangular projection area of the upper block bottom is similar to the aforementioned moving board of the white group circle lattice. The same projection area on the top of the lower block can be imagined as being fixed to the ground, similar to the aforementioned ground board of the black circle lattice.
FIG. 1B is an isometric view showing the two representative prior-art toy blocks detached from each other.
Referring to FIGS. 1A and 1B, a prior-art toy block 10 representing its system has the following features:                A box-shaped body 11;        A stud 12, as an example of other studs on the toy block (similar to one of the aforementioned black circles of the black group lattice), being on a top surface (similar to the aforementioned ground board);        An open space 13, as the hollow interior of the box-shaped body 11, shown on the bottom (similar to the aforementioned moving board);        A bottom post 14 similar to one of the aforementioned white circles in the white group lattice) being in the shape of a tube, as an example of other bottom posts on the prior-art toy block; and        A stopper 15, as an example of other stoppers on the prior-art toy block, being incorporated in the open space 13.        
When two of the mating prior-art toy blocks 10 are being assembled (or stacked up one on top of the other), the bottom post 14 inside the box-shaped body 11, and the mating stud 12 come to be engaged to each other, with the mating stud 12 only abutting against three abutment points—that is, the tangents between the edge of the mating stud against:                an edge of the bottom post 14; and        one edge each on two neighboring stoppers 15.        
The number of abutments with the prior-art system is even less than the aforementioned defined set of existing four abutments. Accordingly, the bond inbetween the stud 12 and its three abutments are not as firm as may be desired. As a consequence, the interference fit inbetween the stud 12 at the three abutment points will need to be significant in order to achieve the required firmness of bond under only three abutments. After some use, the engagement bond between the two prior art toy blocks 10 would deteriorate due to friction wear and stress fatigue over time resulting in the prior-art toy blocks 10 becoming loosely engaged upon assembling.
Another shortcoming with the prior-art system is that only the top of the representative prior-art toy block 10 can be engaged with the bottom of its mating block, making the number of combinations with the assembly variety under such system limited.
In addition, FIG. 1C is an isometric view showing the “actual” condition of two mating prior-art toy blocks as joined (stacked up) one on top of the other. The stud 12 is being friction-held only by the three abutting points c1, c2, c3 for binding the toy blocks 10 together. In other words, the bond between the two mating prior-art toy blocks 10 therefore will depend upon the degree of interference fit of the stud against the stopper 15 and against the bottom post 14. As a consequence, the greater the degree (or the level) of interference fit between the stud 12 and the stopper 15 need to be increased for a firm bond, the greater the compression force from the engaged studs coming to exert onto the stopper 15, causing the stopper 15 to bulge outwardly, thereby forming a bulge 11A on the exterior wall of the box-shaped body 11. This will lead to deformation of the box-shaped body 11, consequently further causes causing another shortcoming as explained below.
Please refer to FIG. 1D. FIG. 1D is a schematic side view showing three mating prior-art toy blocks 10 being joined together in an interlocked fashion. In order to accommodate for the bulge 11A expanding outwards onto the sidewall, which is a result of the interference fit between the stud and the stopper, a 10A (shown in FIG. 1E) between two neighboring toy blocks 10 needs to be provided. As a consequence, this gap 10A further leads to weakened strength and integrity of the entire assembly, making insecure joining of the assembly, which tends to disengage upon impact or upon dropping on hard ground.
Accordingly, the subject of how to firmly engage the mating toy blocks with each other, to increase the service life, to a stronger engagement bond, and to a better integrity of the whole toy block assembly when being subjected to external force is worth considering by those skilled in the art.